### How far should place the lens from the slide

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Q. A slide projector needs to create a 96 cm high image of a 2.0 cm tall slide. The screen is 280 cm from the slide. Assume that it is a thin lens. what focal length does the lens need? How far should you place the lens from the slide?

Q. On a spacecraft two engines fire for a time of 550 s. One gives the craft an acceleration in the x direction of ax = 5.10 m/s2, while the other produces an acceleration in the y direction of ay = 7.30 m/s2. At the end of the firing period, the craft has velocity components of vx = 3660 m/s and vy = 4154 m/s. Find the magnitude and direction of the initial velocity. Express the direction as an angle with respect to the +x axis.

A motorcycle daredevil is attempting to jump across as many buses as possible (see the drawing). The takeoff ramp makes an angle θ = 17.0° above the horizontal, and the landing ramp is identical to the takeoff ramp. The buses are parked side by side, and each bus is 2.74 m wide. The cyclist leaves the ramp with a speed of v = 32.5 m/s. What is the maximum number of buses over which the cyclist can jump?

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